Method of calculation of initial design parameters of microscope objective lenses with a long working distance

We describe an analytic method of the initial design of microscope objectives with a long working distance. The optical system of a microscope objective is composed of two thin optical elements and a frontal optical element from several thick lenses. The paper describes formulas that make it possible to calculate fundamental parameters of the objective, namely Seidel aberration coefficients, radii of curvature, refractive indices of individual lenses of the microscope objective, etc. The proposed method of calculation of the initial design parameters of the microscope objective, which is based on the theory of aberrations of the third order and chromatic aberrations of the first order, enables us to obtain a good starting design for further optimization using optical design software. The method of the design is presented in an example of the microscope objective with a long working distance.